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Table 4 A summary of the estimation results for the parameters Θ

From: Tie-formation process within the communities of the Japanese production network: application of an exponential random graph model

Attributes

\(\overline {\Theta }_{MLE}\)

\(\Theta _{MLE}^{max}\)

\(\Theta _{MLE}^{min}\)

s.d. (ΘMLE)

nonsig.

positive

negative

Endogenous attributes:

       

Reciprocity

1.59

3.78

-2.62

1.31

15%

80%

5%

Popularity (k-in-stars)

3.68

8.25

0.90

1.79

8%

92%

0%

Activity (k-out-stars)

-1.48

-0.66

-4.32

0.81

14%

0%

86%

k-two-paths

-0.01

0.41

-1.00

0.15

60%

28%

12%

Cyclic closure (AT-C)

-0.06

0.56

-2.14

0.26

59%

10%

31%

Path closure (AT-T)

0.00

0.31

-1.38

0.24

48%

40%

12%

Activity closure (AT-U)

-0.09

0.35

-1.58

0.40

39%

37%

24%

Popularity closure (AT-D)

-0.28

0.31

-3.38

0.51

50%

6%

44%

Exogenous attributes:

       

Sector homophily

0.19

2.58

-0.43

0.45

41%

42%

17%

Location homophily

0.86

3.68

0.13

0.72

9%

91%

0%

Bank homophily

0.44

0.14

3.12

0.002

15%

80%

5%

Size heterophily

3.04·10−4

9.02·10−3

-6.15. 10−03

1.12·10−03

48%

33%

19%

Sales heterophily

3.59·10−8

5.31·10−7

4.31. 10−10

7.26·10−08

21%

79%

0%

Sales receiver effect

5.80·10−8

1.22·10−6

4.73. 10−10

1.50·10−07

22%

78%

0%

Sales sender effect

− 1.31·10−8

− 1.18·10−10

-3.37. 10−07

3.71·10−08

52%

0%

48%

  1. The results for each parameter are given based on the 100 considered communities in the Japanese production network. A parameter is considered significant for a Wald ratio of ≥ 2. Significance is rejected for a Wald ratio of < 2. The entry in the significance column (sig.) is + if the parameter is significant and otherwise